To expand on the answers already provided:
The basic isue is that the criminal and civil trials really address very separate questions.
Remember, in the crimiinal trial, the design is that it's not even the accused versus the victime, it's 'the people' as the prosecutor.
It's a very specific process about determining violation of the crimnal law on specific code violations.
The civil trial addresses the amount owed with minimal relation to any criminal law - it's about contracts and other harms and remedies.
It's a very different matter to be discussing the finer points of the woman's criminal culpability in the attack - her state of mind, intent, and other matters - from the question of what she should have to pay to compensate the victim apart from any criminal fines, which uses different standards of proof (beyond a reasonable doubt for criminal, preonderance of the evidence for civil), has different evidence rules, typically a different jury size and vote requirement (unanimous requirement for criminal, typically not for civil), and so on.
Just because the attack has both criminal and civil issues doens't mean it makes sense to use the same trial.
The main relationship between the two is that given the higher standard of proof for criminal trials, civil trials often wait for the criminal trial and use that as evidence.
It's very convenient for plaintiffs to be able to save proving guilt at the civil trial and simply point to the criminal conviction, and get to the damages.
The only reasons the plaintiff normally would only owe 2K instead of the full medical bills would be the judge deciding that the blame was divided, or that not all the bills were legitimate for charging to the defendant (for example, if the bill was padded), or a limit on the court's damages (small claims court for example typically has a limit of 5K or a little more, but I doubt the limit is 2k).
The RIAA analogy just muddies the waters on your main question IMO. You can always have that sort of thing, that makes it more of a rant.
'We can put a man on the moon, but we can't (fill in your pet peeve government isn't doing how you want)'.
RIAA has a lot more to do with societal issues, technology, and politics than with the courts.
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